## 1 INTRODUCTION

The heating of buildings represents over one-fifth of the EU's energy consumption. Achieving the net-zero emission target of the Paris Agreement by 2050 requires a stronger focus on reducing the building sector's emissions (European Commission, 2016; IEA, 2022a). Various strategies exist to reduce building emissions from demand-side efficiency measures to clean and renewable energy sources. Utilizing heat pumps is effective for heat supply (IEA, 2021a, 2021b, 2022a, 2022b), offering versatility and scalability across building types (Bloess et al., 2018; Schaber et al., 2013). In district heating systems, HPs can improve not only decarbonization but also improve economic and environmental performance (Barco-Burgos et al., 2022) and decrease primary energy consumption (Ayou et al., 2023). Approaching zero fossil fuel electricity production in the Nordic countries by 2030 will support the electrification of heating through heat pumps, also contributing to emission reduction. Geothermal heat is of special interest in both the electricity and heat sectors. In areas with significant geothermal potential, such as Tenerife, geothermal energy could potentially meet even up to close to 30% of the island's electricity demand (Montesdeoca-Martínez & Velázquez-Medina, 2023). As a heat source for heat pumps, lower-temperature geothermal heat can not only provide continuous heat output during the heating season but also function as a heat sink in the summer. Additionally, geothermal energy is an environmentally friendly energy source (Laloui & Rotta Loria, 2020; Rybach, 2003). In a GSHP (ground source heat pump) system, the coefficient of performance (*COP*) typically varies between 3 and 5 (Zhang et al., 2022), which enables major fuel and emission savings.

During recent years, the progress in larger GSHP systems, featuring deeper boreholes, has been noticeable (Gehlin et al., 2016; Todorov et al., 2021; Xue et al., 2023). For example, a major logistics center in Finland employs 150 borehole heat exchangers (BHEs), each 300 m deep, for GSHP (Gehlin et al., 2016). In Espoo (Finland), a 74-unit borehole field is considered (Todorov et al., 2021). However, implementing large borehole field systems with such shallow BHEs faces challenges due to extensive surface requirements and on-site probe placement limitations. As of 2019, Kallio (2019) reported 20–25 large-scale GSHP applications in Finland with a total borehole length exceeding 10 km. Gehlin underscored that the Scandinavian geology could enable deeper boreholes making GSHPs suitable for densely populated urban areas (Gehlin et al., 2016). Rybach et al. proposed the deep borehole heat exchanger (DBHE) concept involving vertical 2–3 km deep boreholes with a coaxial pipe (Rybach & Hopkirk, 1995) This concept has also attracted interest in northern China (Cai et al., 2021; Deng et al., 2019) However, full exploitation of such deep boreholes would require more profound understanding of their performance in different operational conditions typical to varying heat load types.

Designing and optimizing BHE systems require accurate modeling of their performance. The heat extraction from boreholes can be designed and modeled with computer tools such as earth energy designer (EED) (Hellström, 1997) and GLHEPRO (Xu, 2005). However, these may not be suitable for the most complex BHE simulations, which require consideration of factors, such as groundwater flow or heat transfer within deeper rock formations, which could affect the estimates of extractable heat. For such complex cases, more advanced models and numerical solutions are needed such as the numerical model element Type 285 in the TRNSYS 18 program (Antelmi et al., 2023), which enables simulating BHEs affected by groundwater flows, also validated against hydrogeological models like MODFLOW and experimental data. The results from TRNSYS demonstrated an increase in exchanged heat between the BHE and subsoil with higher groundwater flow velocities. For more complex geometries, cases, and analyses, modeling approaches based on finite difference or finite element modeling of the ground and BHE can offer further improvements. Software packages, such as FEFLOW (Diersch, 2014), MODFLOW (Hughes et al., 2022), or COMSOL (COMSOL) (utilized in this paper), include the necessary capabilities for such advanced simulations.

In terms of the definition of deep borehole exchangers, previous studies have used a depth range of 1 km (Holmberg et al., 2016), 0.6–3.0 km (Piipponen et al., 2022), and 2–3 km (Kohl et al., 2002). Here, we use a depth range from 0.8 to 2.0 km for DBHE. The thermal efficiency of the deeper heat exchanger is adversely affected by increasing thermal short-circuiting between the upward and downward flows in the BHE. Also, the pressure drops in the hole increased causing higher pumping energy consumption when using U-pipes with borehole depth approaching 500 m. DBHE utilizes a coaxial collector pipe, which sets it apart from the U-tube collector pipes typically employed in shallow borehole exchangers (Kohl et al., 2002; Pan et al., 2020).

The thermal performance of DBHE systems has been studied at concept and sizing levels. For example, Pan et al. (2020) and Piipponen et al. (2022). analyzed the spatial heat extraction rate in different regions of Finland, and Holmberg (Xue et al., 2023) analyzed the effect of the geothermal gradient on the heat yield. Previous studies have, however, mainly focused more on refining the DBHE concept, while the investigation of specific usage scenarios has been relatively limited. The questions of how heat extraction, heat demand profile, operating conditions, and the application will impact the performance of deep borehole exchangers have received less attention but will be investigated in this paper through numerical simulations. Such information is highly important for optimal sizing and use of deep borehole exchangers in different applications and to broaden their applicability and assess their profitability. Since different operational scenarios affect the heat output from DBHE and hence also its economics, a brief economic comparison is made here based on the thermal simulation results. In the present paper, DBHE is analyzed using an advanced numerical model with the finite element method (FEM). The modeling software COMSOL Multiphysics® is employed for this purpose.

This paper emphasizes the central role of operational scenarios of DBHE. The suitability of deep boreholes for base heat production, seasonal production, and production following a district heating profile will be assessed through numerical modeling. The paper describes first the methodology and modeling approach in Section 2, then the results in Section 8, and finally Section 13 outlines the conclusions.

## 2 METHODOLOGY

In this section, a brief description of the DBHE principle and the governing physical equations in the model are presented. Model validation and the parameters used in the analysis are also discussed.

### 2.1 Model description

The DBHE system comprises a drilled borehole into the ground, an installed coaxial pipe, and a heat pump that raises the water extracted from the DBHE to the desired temperature, serving both space and domestic hot water requirements. Deeper heat exchangers face challenges, such as increasing thermal short-circuiting and pressure drops, especially when using U-pipes at depths approaching 500 m. Notably, DBHE utilizes a coaxial collector pipe, distinguishing them from the U-tube collector pipes used in shallow borehole exchangers (Kohl et al., 2002; Pan et al., 2020). To extract heat from DBHE, water is injected through the annulus pipe and the heated water is then pumped up through the inner pipe. According to Holmberg et al., this direction was found the most effective (Holmberg et al., 2016).

For the thermal analyses of the DBHE under different operational scenarios, a numerical model was developed in the COMSOL Multiphysics® program (COMSOL, 2021). DBHE simulations have been successfully conducted using COMSOL Multiphysics® (Piipponen et al., 2022), in addition to other commercial and open-source modeling software (Cai et al., 2021). COMSOL Multiphysics® relies on the FEM and the discretization of the geometric DBHE model into smaller elements is accomplished through the use of Mesh. Users have the flexibility to choose element types and sizes, either from predefined options or by specifying them individually. These choices directly impact the computation time of the simulation, underscoring the importance of selecting an efficient element type. In the simulations presented in this paper, the Mesh has been defined in a way that utilizes a finer element size close to the borehole and a coarser mesh more distant from the DBHE. While the used Mesh has a slight influence on the results, its impact is discussed in more detail later in this paper.

The COMSOL model has been presented in detail in Lund (

2019). A three-dimensional geometrical model of the coaxial BHE and the surrounding rock in COMSOL are physically coupled. The governing general equation of heat transfer in solid used here is the following:

(1)

where

*ρ*
g is density of ground (kg/m

3),

*c*
p is specific heat capacity (J · kg

−1 · K

−1),

*T* is absolute temperature (K),

*u*
trans is velocity vector of translational motion (m/s),

*q* is heat flux by conduction (W/m

2),

*q*
r is heat flux by radiation (W/m

2),

*α* is coefficient of thermal expansion (1/K),

*S* is second Piola-Kirchhoff stress tensor (Pa), and

*Q* is additional heat sources (W/m

3). Symbol : in Equation (

1) stands for double dot product. For our case with solid rock, the term
is zero in Equation (

1).

The heat transfer in the borehole includes two components: the pipe annulus and the inner pipe. The fluid temperature

*T*
f in the pipe can be solved from the energy equation for an incompressible fluid flowing in a pipe (Incropera,

2015; Lurie,

2009):

(2)

where

*ρ*
f is density of fluid (kg/m

3),

*A* is pipe cross-sectional area for flow (m

2),
is velocity field (m/s),

*k* is thermal conductivity (W · m

−1 · K

−1),

*d*
h is hydraulic diameter (m),

*f*
D is friction factor,

*Q*' is general heat source (W/m), and

*Q*'

wall is external heat exchange through pipe wall (W/m).

The above equations are solved with the FEM. The main COMSOL Multiphysics modules used were “Heat transfer in solids” and “Heat transfer in Pipes.”

The power extracted from the borehole (

*Φ*) is directly proportional to the temperature change between the input and output temperatures of the fluid circulating in the BHE:

(3)

where
is the mass flow of the injected circulating fluid (kg/s),

*T*
in is the inlet temperature of the fluid (°C), and

*T*
out is the outlet temperature of the fluid (°C).

When connecting the BHE to the heat pump (HP) through a circulation network, the fluid heated in the BHE is fed to the heat pump evaporator, where it releases heat and cools down before being returned to the BHE. The thermal output from the heat pump's condenser can be calculated as follows (Wilkie,

1973)

(4)

where

*Q*
h is the thermal output from the heat pump's condenser,

*Q*
c is the heat absorbed from the source (e.g., ground), and

*W* is the work done by the compressor.

The theoretical

*COP* of the heat pump can be calculated through the Carnot process, where the theoretical limit for the

*COP* of a heat pump operating between heat source and sink with constant temperatures is the following (Laitinen et al.,

2014):

(5)

where

*T*
c is the evaporator temperature (K) and

*T*
h is the condenser temperature (K).

To calculate the *COP* in real conditions, it has been proposed that the theoretical *COP* is multiplied by the loss factor of the compressor to consider the heating process losses of the heat pump. The loss factor is calculated by dividing the measured heat pump *COP* by the theoretical heat pump *COP* (Laitinen et al., 2014).

While measured *COP* values were not available, the ideal *COP* in Equation (5) is multiplied by two loss factors: *η*CA is the Carnot non-ideality factor (0.45–0.55) and *η*m is the mechanical efficiency of the compressor (0.90–0.95) (Lund, 1984). Because of losses in the heat exchanger and piping network, and nonideal heat transfer, the temperatures of the heat source and the application cannot directly be applied in Equation (5). A 5–10 K adjustment (d*T*) is typically needed both for the condensing and evaporating temperatures.

### 2.2 Model validation

To investigate the proposed scientific questions, it is essential to validate the numerical model that covers all features of a DBHE array. The numerical model built here in COMSOL Multiphysics is compared with the numerical model employed by Holmberg et al. (2016), which was used to replicate the measurements from the experimental distributed thermal response test. For the validation, parameters consistent with Holmberg's work have been employed, specifically for case *D*0 = 140 mm and center pipe dimensions equal to 90 mm in diameter and a wall thickness of 5.1 mm. The validation results are shown in Figure 1.

In comparison to the solution presented by Holmberg et al., the difference between the models at 300 m was 21%, 11% at 500 m, 8% at 700 m, and 6% at 1000 m (Figure 1). Notably, the present model slightly underestimated heat output for shallower boreholes and overestimated at increasing depth compared to Holmberg's model. This variation is likely attributed to the mesh employed in the simulations. Reducing the element size mitigates the discrepancy down to 2% at 500 m. However, this improvement comes at a considerable expense in the computational time, with the simulation duration being fivefold. In the context of modeling deeper boreholes with depths exceeding 1000 m, our findings indicate that the present model achieves a satisfactory level of accuracy for the intended scientific objectives.

### 2.3 Model setup

#### 2.3.1 Model parameters

The main parameters of the DBHE model are given in Tables 1 and 2. The chosen site parameters are typical for the geological conditions in Finland. Water is used as the heat carrier fluid circulating downward through the annulus pipe and upward through the center pipe following the design by Horne (1980). The overall simulation time is set at 25 years. Groundwater zones are assumed absent in the deeper bedrock, with the initial 300 m of the borehole being cased to prevent potential infiltration to groundwater. The concrete casing's low thermal conductivity acts as insulation, and thus, potential groundwater flow is not considered in this study, aligning with the optimization goal of maximizing the utilization of the DBHE (Piipponen et al., 2022).

Table 1. Parameters of deep coaxial borehole exchanger.
Parameter |
Value |

Type of fluid |
Water |

Depth of borehole (km) |
1–2 |

Mass flow rate (kg/s) |
15 |

Thermal conductivity of inner pipe (W · m−1 · K−1) |
0.42 |

Diameter of inner pipe (mm) |
90 |

Diameter of outer pipe (mm) |
200 |

Inlet temperature of the fluid (°C) |
2 |

Inlet temperature of the fluid (heat injection) (°C) |
40 |

Table 2. Parameters of bedrock.
Parameter |
Value |

Geothermal gradient (°C/km) |
20 |

Thermal conductivity (W · m−1 · K−1) |
3 |

Volumetric heat capacity (MJ · m−3 · K−1) |
2.16 |

Average ground surface temperature (°C) |
6.8 |

Geothermal heat flux (W/m2) |
0.05 |

The initial soil temperature is determined by the geothermal gradient assuming a constant ground surface temperature (Piipponen et al., 2022). The geothermal gradient is set at 20°C/km, within the observed range of 11.0–24.6°C/km in Finland (Puranen et al., 1968). It is modeled as linear and stable.

Pipe dimensions and mass flow rates are selected to facilitate high mass flow, minimize thermal short-circuiting, and ensure reasonable pressure losses in the system. The output temperature from the DBHE is upgraded to 60°C using a heat pump. The *COP* is calculated with Equation (5) using *η*CA = 0.45, *η*m = 0.90–0.95.

#### 2.3.2 Simulated scenarios

The analyses comprise performance simulation of 1–2 km deep borehole exchangers focusing on the energy perspective, that is, power and energy extracted from the DBHE in four different heat usage scenarios.

The heat flow profiles used in the analysis are the following:

1.

Constant flow profile: Heat is extracted from the DBHE with a continuous 15 kg/s mass flow rate. This emulates a bottom-cycle for district heating (DH) production aiming at high full-hours a year.

2.

2-step constant flow profile: A constant mass flow rate is applied as in the previous case, except for the summer months (June–August), when the boreholes are not used for 90 days (2160 h), that is, the mass flow rate is set to zero, which also allows natural heat regeneration of the rock. This resembles a case in which some other heat source is used in the summer during low heat demand.

3.

2-step constant flow profile with heat injection into the DBHE: Similar to the previous 2-step constant flow profile, but it is assumed that there is excess heat available for charging the DBHE in the summer.

4.

Varying heating flow profile: The mass flow rate varies over time based on the relative shares of heat consumption of Helsinki's district heating (Helen Oy, 2021). Monthly energy quantities are normalized by dividing them by the highest value, yielding relative shares. The relative shares are then multiplied by the maximum mass flow rate to get averaged monthly mass flow rates (Figure 2). The maximum mass flow rate, occurring during the peak consumption month is 15 kg/s.

In addition, the importance of the time interval in heat extraction and the heat injection temperature in the “2-step constant flow” case was assessed.

A preliminary economic analysis is also conducted for the different heat flow scenarios. The value of the heat from DBHE was assumed to follow the district heat profile of Helen Ltd., which supplies the DH in Helsinki. The profile is shown in Figure 2. In the analysis, the maximum value of heat (January) was set at 40 and 60 €/(MW·h), and the values of the remaining months were scaled in relation to the monthly shares of the maximum DH load (=100%) in Helsinki. The profile is shown in Figure 2.

## 3 RESULTS AND DISCUSSION

In the following, the main results of the analysis are presented. DBHEs with a depth of 1–2 km are considered using four different heating profiles: constant, two-step constant flow without and with heat injection, and varying mass flow profiles. In the analyses, the average power extracted from the borehole over the whole cycle (1 year), average extracted power during the active operational time (excludes idle time and injection of heat), as well as the maximum and minimum values during the active operational time are used to judge the performance. These are illustrated as an example in a 2-step constant flow profile (Figure 3).

### 3.1 Heat extraction analysis

Figure 4 illustrates the yearly thermal energy production and Figure 5 the average yearly power for the four cases. The highest energy yield and power level are achieved with the constant flow profile, where DBHE operates continuously at full mass flow rate, but the results are quite close to the 2-step flow case with 3 months of heat recharge/injection into the DBHE.

Summertime heat injection increases the energy output by 13%–25% compared to no recharging. The impact of DBHE charging diminishes with increasing depth when the injection temperature is held constant at 40°C. This is attributed to the geothermal gradient (20°C/km). At a DBHE depth of 1 km, the bottom temperature is approximately 20°C, whereas at a 2 km DBHE, it is 40°C. Consequently, a constant injection temperature of 40°C has a higher relative charging effect on a 1 km than a 2 km DBHE. To achieve the same relative charging effect for a 2 km DBHE, a higher injection temperature would be required.

The 2-step flow strategy reaches the highest power output during the active operational time. This is demonstrated in Figure 6 in which the inactive heat extraction time of the DBHE has been excluded from the calculated average power. In this case, the 2-step flow case with heat injection emerges as the best option yielding 24%–35% higher power output than the constant flow scenario. Even without heat injection, the 2-step flow case performs the best (6.0%–7.5% higher) making this option useful to cut peak thermal power demand during the heating season.

In scenarios involving heat injection to the borehole, the instantaneous maximum power at the beginning of the 2-step flow cycle is 80%–107% higher compared to the constant flow power. Similarly, in scenarios without injection, the 2-step function demonstrates a notable advantage, yielding about 23%–30% more output power than the constant flow. Noteworthy is also that the 2-step flow case gives the highest power output from the onset forwards irrespective of charging. Also, the power at the end (=active MIN power) surpasses the average power of the constant flow. This means that throughout each phase of the cycle, the 2-step function extracts more power from the DBHE compared to the continuous operation with constant flow. This shows that the performance dynamics affect the potential benefit and efficiency of DBHE.

The above results have several implications on how the thermal performance of DBHE could be improved. First, natural regeneration of the borehole through a pause in the heat extraction leads to higher thermal power output, though also to slightly lower overall heat extraction. If excess heat were available for heat injection, this would also increase the total heat extraction. The constant flow mode yields better performance than a varying flow adjusted to the heat demand, but would also require finding additional uses for heat in the summer months, for example, through coupling to regional networks. In this case, the flow pattern starts to approach the 2-step flow case, in which a higher heating power output could be generated even during the heating season also replacing fossil-based boilers. As the varying flow case showed the lowest performance of the four cases studied, this could lead to practical applications to oversizing DBHE and traditional shallower boreholes could therefore potentially offer a better outcome in this case. The above considerations underline the importance of system integration of DBHE with other energy processes for optimizing its overall effectiveness.

### 3.2 Two-step flow sensitivity analysis

The 2-step flow function case enables the DBHE to remain idle or to function as heat storage through heat injection. Key operational parameters, that is, time of no heat extraction and injected heat temperature, will influence the power and energy level of extracted heat from the DBHE. A crucial question is also for how long time would (free) waste heat be available. Therefore, a sensitivity analysis was undertaken to study the influence of these parameters in more detail for the 2-step constant flow scheme:

1.

9 months heat extraction from DBHE and 3 months idle (base case for 2-step constant flow);

2.

6 months heat extraction from DBHE and 6 months idle;

3.

9 months heat extraction from DBHE and 3 months heat injection (base case for 2-step constant flow with heat injection);

4.

6 months heat extraction from DBHE and 6 months heat injection;

5.

3 months heat extraction from DBHE and 9 months heat injection (e.g., for peak power).

Figure 7 illustrates the heat extraction rate for the above cases, which shows that the average power level during heat extraction only marginally increases with increased idle time, or 7%–8% for an extra 3 months of rest.

Through heat injection (40°C), major benefits were achieved when increasing the injection time. An increase in injection time from 3 months to 6 months resulted in a 16%–21% increase in active operational heat extraction power while extending the injection time from 3 to 9 months yields a substantial increase of 31%–40%. Despite the potential for higher power outputs through extended idle or injection months, the heat energy extraction from the well significantly declines compared to the base scenario (9 months extraction/3 months idle/injection), due to the shorter heat extraction period. This is illustrated in Figure 8. In the 2-step flow scenario without heat injection, extracted heat energy decreases by 30% when increasing from 3 to 6 idle months. In the heat injection scenario, roughly 20% reduction is observed in this case. However, when the operational extraction time is reduced by 6 months in the heat injection scenario, the extracted heat output is reduced by 57%–61%, indicating a nonlinear relationship in the extraction time. The above cases will increase the peak power supply from the borehole, but the profitability of these schemes will depend on whether the higher revenue during peak conditions will compensate for the income stream lost during the remaining time with lower revenue levels.

Next, the temperature of the waste heat source used for heat injection was raised from 40 to 60°C, as shown in Figure 9. Increasing the injection temperature along with adding 3 months more to injection time (6/6 months) resulted in close to the same extracted heat as in the base case (9/3 months). Active operational heat extraction power increases by 35%–47%. Particularly for shallower DBHE systems, recharging at 60°C yields almost as much energy as the 9/3 months scenario at 40°C. From an economic perspective, prioritizing heat extraction in the winter months could offer better financial returns in this case. However, extending the charging time to 9 months at 60°C yielded less extracted heat than in the base case due to the lower heat storage efficiency of the injected heat, though the active operational extraction power increased by 42%–54%. Hence, a more optimal charging efficiency is achieved when the charging time is kept moderate. In the above examples, a 6-month charging time performs still well.

### 3.3 *COP* of the heat pump with DBHE

The output temperature from the borehole will affect the performance of the heat pump. Using Equation(5) and assuming a 60°C condenser temperature and a temperature adjustment of d*T* = 5 K enables us to estimate the *COP* of the heat pump for the different operational modes investigated in this paper. The outcome is shown in Figure 10. The results clearly show that the modes with the least energy extraction from the borehole yield the highest average *COP* due to the higher output temperature from the borehole. The difference increases with borehole depth: at 1 km the difference between the best and worst case is 1%, and at 2 km 3%.

The constant flow exhibits the lowest *COP* among the considered cases, but if regenerated with heat injection for 3 months, the *COP* could be improved by 1.2% for a 2 km well.

However, the differences in the *COP* with the various operational modes are still marginal to have a major effect on the operational costs. Therefore, for the overall energy optimization of the DBHE, the interplay between the other operational parameters is more important.

### 3.4 Tentative economic analysis

A full economic analysis of the DBHE system was outside the scope of the present study. In addition, reliable data on the DBHE cost is still not readily available. Instead, the effect of the operational mode on the revenue generation was assessed indicating the economics of the operational side. The revenue was described in Chapter 2 assuming two revenue levels at peak power in January (40 and 60 € · MW−1 · h−1), which is scaled in relation to the heat load for the other months. Figure 11 summarizes the results from the economic analysis.

The varying heating flow yields the lowest revenue, even though it operates at full capacity when the monthly value for the heat is at the highest. This leads to a rather intriguing conclusion: the highest energy yield does not necessarily equate to the greatest revenue, especially with a seasonally strongly varying heat load. The constant flow and 2-step flow result in almost equal financial results, even though the constant flow produces more energy, which is due to the low value of summertime heat. The highest yearly revenue is obtained when the DBHE is regenerated with heat in the summer, despite the revenue loss during the summer months. This assumes, however, that the excess heat for injection is almost free during the summer months. For shallower DBHE with heat injection case, a 22% better return is achieved, which decreases to 12% as the well depth increases. It should be noted that the results were scaled to the length of the DBHE meaning that the total revenue of a DBHE increases with the length of the borehole.

## 4 CONCLUSION

The effect of different heat extraction profiles and operating strategies on the thermal performance of DBHE for heating has been analyzed.

The operating mode chosen significantly affects both the thermal and economic performance of DBHE. A longer operating time for a full cycle generally leads to higher yearly heat extraction from DBHE (up to 43% more between best and worst scenario), while shorter operating time can result in higher instantaneous thermal power output during active heat extraction, but lower heat energy yield. An optimal operating strategy of DBHE should strive to maximize the operating time or regenerate the borehole during low heating demand (summer). For example, with heat injection for 3 months, nearly the same amount of heat could be extracted for 6 months, but at a higher power level as with a constant flow strategy throughout the year. For a short time period, it would be possible to reach even up to a 107% increase in the extracted heat power from DBHE. A higher thermal output from DBHE during the heating season could reduce the need for peak boilers in heating.

A varying flow profile following the heat demand yields 30% less heat than a constant profile, though it can achieve a higher power output level. A completely idle off-period of DBHE for 3 months was more efficient than running at reduced capacity for most of the time as in the varying flow case.

The choice of operating mode in practice will depend on the prevailing conditions and heat demand. The findings in this paper provide insight and guidelines to optimize the performance of DBHE. The results also demonstrate that DBHEs are a highly potential clean energy technology for larger heat loads.

This study was based on computational models and numerical simulations. Real operational data from pilot plants underway in Scandinavian conditions would be valuable in the future to assess the thermal performance and the competitiveness of DBHEs more accurately against traditional heating systems.